Patterns for Model Structure

Daniel Vartanian

University of São Paulo

August 13, 2025

Hi there! 👋

In this presentation, I will provide an overview on Pattern-Oriented Modeling—an approach for designing structurally realistic models.

We’ll explore the following topics:

1. Introduction
2. Pattern-Oriented Modeling
3. How to Start
4. Example

Introduction

What Is a Model?

A model is a simplified representation of a system. It can be conceptual, verbal, diagrammatic, physical, or formal (mathematical) (Sayama, 2015).

A good model is simple, valid, and robust (Sayama, 2015).

All models are wrong, but some are useful (Box, 1979, p. 202).

“We use models as simplified and purposeful representations to answer research questions and solve problems. A “simplified representation” means that we use only a limited and preferably small number of variables to represent the real system” (Railsback & Grimm, 2019, p. 233)

\(+\) Variables \(\rightarrow\) \(+\) Complex

“Models in general and ABMs in particular should therefore be as simple as possible and use the most parsimonious representation that still captures key characteristics and behaviors of a real system” (Railsback & Grimm, 2019, p. 233)

Structurally realistic models

Power Laws & Factor Sparsity

Power laws (\(y = ax^{-k}\))

Pareto’s/Zipf’s distributions

~80/20 rule: 80% of the effects come from 20% of the causes.

[…] the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people’s personal fortunes all appear to follow power laws (Newman, 2005).

Top U.S. retail companies by market cap as of September 2024

The Modeling Cycle

1. Formulate the question
2. Assemble hypotheses for essential processes and structures
3. Choose scales, entities, state variables, processes, and parameters
4. Implement the model
5. Analyze, test, and revise the model
6. Communicate the model

Pattern-Oriented Modeling

Patterns

A pattern is anything beyond random variation.

We can think of patterns as regularities, signals.

Alignment: A bird tends to turn so that it is moving in the same direction that nearby birds are moving.

Separation: A bird will turn to avoid another bird which gets too close.

Cohesion: A bird will move towards other nearby birds (unless another bird is too close).

Pattern-Oriented Modeling

Pattern-Oriented Modeling (POM) is the use of patterns observed in the real system as the additional information we need to make ABMs structurally realistic and, therefore, more general, useful, scientific, and accurate.

Pattern-oriented model design. Observed patterns that characterize old-growth beech forests [(A); images: front, M. Flade; right, C. Rademacher; top, S. Winter] include a horizontal mosaic of developmental stages [(B); x scale: 400 m; modified from (42)], the vertical patterns of tree size that define the developmental stages [(C), showing the late decaying stage; x scale: ~60 m; modified from (43)], and distributions of fallen large trees [(D), a map of fallen wood; ellipses indicate crown projections of standing trees; x scale: ~60 m; modified from (43)]. To allow these patterns to emerge from it, the model includes a grid-based horizontal structure [(E), showing grid cells in three developmental stages; x scale: 570 m), a grid-based vertical structure [(F), showing each grid cell’s percentage cover for four height classes; total area shown: 1 ha)], and individual representation of large trees [(G), showing one cell’s trees in the largest two height classes; cell area: 204 m²); (E) to (G) modified from (18)]. (Grimm et al., 2005, Figure 2)

Filters

A filter sepa­rates things, such as models that do and do not reproduce the cyclic pattern. The basic idea of POM is to use multiple patterns to design and analyze models.

A small number of weak and qualitative but diverse patterns that characterize a system with respect to the modeling problem can be as powerful a filter as one very strong pattern, and are often easier to obtain.

For most systems, however, one single pattern is not enough to decode the internal organi­zation. Multiple patterns, or filters, are needed.

Nonrealistic Models

ODD Protocol

Overview

1. Purpose and Patterns
2. Entities, State Variables, and Scales
3. Process Overview and Scheduling

Design Concepts

1. Basic Principles
2. Emergence
3. Adaptation
4. Objectives
5. Learning
6. Prediction
7. Sensing
8. Interaction
9. Stochasticity
10. Collectives
11. Observation

Details

1. Initialization
2. Input Data
3. Submodels

How to Start

Ok, But How?

How do you identify a set of diverse patterns that characterize the system for the problem that you are modeling?

This task, like much of modeling, uses judgment, knowledge of the sys­tem, and often, trial and error.

1. Start by formulating your model (writing a description of it using the ODD protocol), with the purpose of the model as the only filter for designing the model structure.
2. Identify a set of observed patterns that you believe characterize your system relative to the problem you model.
3. Define criteria for pattern-­matching: How will you decide whether the model does or does not reproduce each pattern?
4. Now review your draft model formulation and determine what additional things need to be in the model to make it possible for your characteristic patterns to emerge from it.

Key Questions

Where in the Ecological Hierarchy Can We Find Patterns?

How Should Simulations and Observations Be Compared?

The Modeling Cycle

1. Formulate the question
2. Assemble hypotheses for essential processes and structures
3. Choose scales, entities, state variables, processes, and parameters
4. Implement the model
5. Analyze, test, and revise the model
6. Communicate the model

Example

Abstract versus Empirical Models

Abstract models allow for the examination of general principles in detail (Rand & Wilensky, 2007).

Empirical models are generally more oriented towards prediction and often need to address specific questions posed by policy-makers at particular sites (Sun et al., 2016).

Full spectrum modeling combines the benefits of abstract and empirical models (Rand & Wilensky, 2007).

Simple (Rand & Wilensky, 2007; Sun et al., 2016) or abstract (Sun et al., 2016) models versus photograph (Parker et al., 2003), empirical, complicated (Sun et al., 2016), elaborated and realistic (ER) (Rand & Wilensky, 2007) models.

Simple model example: Schelling’s segregation model (Schelling, 1971).

We call this the ‘Medawar zone’ because Medawar described a similar relation between the difficulty of a scientific problem and its payoff (Grimm et al., 2005).

Question

Does climate change impact the health and nutrition of Brazilian children under five years old?

Conceptual Model

Conceptual model of the environment-food-health nexus among children under five years of age using the complex systems approach: (B) the balancing feedback loop, (R) the reinforcing feedback loop, (+) positive relationship between the factors, (-) negative relationship between the factors.

Conceptual Model

Conceptual model of the environment-food-health nexus among children under five years of age using the complex systems approach: (B) the balancing feedback loop, (R) the reinforcing feedback loop, (+) positive relationship between the factors, (-) negative relationship between the factors.

Patterns

Response in food production to global changes in temperature and precipitation

Response in food accessibility for low-income families to the reduction in food production

Response in healthy food consumption by low-income families to the reduction in food accessibility

Response in health and nutrition of children from low-income families to the reduction in healthy food consumption

Agents

👁️⃤

Observer

Grid Cells

⊞
🌡️
🌧️

Food

🍌🍅
🥬🌾
🥛🥩

Families

👨‍👩‍👧
👩‍👩‍👦
👨‍👨‍👧

Children

🧒
👧

LogoClim

FoodClim

🚧 Under development 🚧

GlobalSyndemic

🚧 Under development 🚧

Closing Remarks

This presentation was created with the Quarto Publishing System. The code and materials are available on GitHub.

References

In accordance with the American Psychological Association (APA) Style, 7th edition.

Box, G. E. P. (1979). Robustness in the strategy of scientific model building. In R. L. Launer & G. N. Wilkinson (Eds.), Robustness in statistics (pp. 201–236). Academic Press. https://doi.org/10.1016/B978-0-12-438150-6.50018-2

Carvalho, A. M. de, Garcia, L. M. T., Lourenço, B. H., Verly Junior, E., Carioca, A. A. F., Jacob, M. C. M., Gomes, S. M., & Sarti, F. M. (2024). Exploring the nexus between food systems and the global syndemic among children under five years of age through the complex systems approach. International Journal of Environmental Research and Public Health, 21(7, 7), 893. https://doi.org/10.3390/ijerph21070893

Gallagher, C. A., Chudzinska, M., Larsen-Gray, A., Pollock, C. J., Sells, S. N., White, P. J. C., & Berger, U. (2021). From theory to practice in pattern-oriented modelling: Identifying and using empirical patterns in predictive models. Biological Reviews, 96(5), 1868–1888. https://doi.org/10.1111/brv.12729

Grimm, V., Revilla, E., Berger, U., Jeltsch, F., Mooij, W. M., Railsback, S. F., Thulke, H.-H., Weiner, J., Wiegand, T., & DeAngelis, D. L. (2005). Pattern-oriented modeling of agent-based complex systems: Lessons from ecology. Science, 310(5750), 987–991. https://doi.org/10.1126/science.1116681

Neuert, C., Rademacher, C., Grundmann, V., Wissel, C., & Grimm, V. (2001). Struktur und Dynamik von Buchenurwäldern: Ergebnisse des regelbasierten Modells BEFORE. Naturschutz und Landschaftsplanung, 33(6), 173–183.

Newman, M. (2005). Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(5), 323–351. https://doi.org/10.1080/00107510500052444

Parker, D. C., Manson, S. M., Janssen, M. A., Hoffmann, M. J., & Deadman, P. (2003). Multi-agent systems for the simulation of land-use and land-cover change: A review. Annals of the Association of American Geographers, 93(2), 314–337. https://doi.org/10.1111/1467-8306.9302004

Railsback, S. F., & Grimm, V. (2019). Agent-based and individual-based modeling: A practical introduction (2nd ed.). Princeton University Press.

Rand, W., & Wilensky, U. (2007). Full spectrum modeling: From simplicity to elaboration and realism in urban pattern formation. North American Association for Computational Social and Organizational Sciences (NAACSOS). http://ccl.northwestern.edu/2007/FullSpectrum.pdf

Reynolds, C. W. (1987). Flocks, herds and schools: A distributed behavioral model. Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, 21, 25–34. https://doi.org/10.1145/37401.37406

Sayama, H. (2015). Introduction to the modeling and analysis of complex systems. Open SUNY Textbooks.

Schelling, T. C. (1971). Dynamic models of segregation. The Journal of Mathematical Sociology, 1(2), 143–186. https://doi.org/10.1080/0022250X.1971.9989794

Sun, Z., Lorscheid, I., Millington, J. D., Lauf, S., Magliocca, N. R., Groeneveld, J., Balbi, S., Nolzen, H., Müller, B., Schulze, J., & Buchmann, C. M. (2016). Simple or complicated agent-based models? A complicated issue. Environmental Modelling & Software, 86, 56–67. https://doi.org/10.1016/j.envsoft.2016.09.006

Vartanian, D., Garcia, L., & Carvalho, A. M. (2025a). FoodClim: Food yield responses to climate change in NetLogo [Computer software]. https://github.com/sustentarea/foodclim

Vartanian, D., Garcia, L., & Carvalho, A. M. (2025b). GlobalSyndemic: Climate change effects on child nutrition in Brazil [Computer software]. https://github.com/sustentarea/globalsyndemic

Vartanian, D., Garcia, L., & Carvalho, A. M. (2025c). LogoClim: WorldClim in NetLogo [Computer software]. https://github.com/sustentarea/logoclim

Wilensky, U. (1998). Flocking model [Computer software]. Center for Connected Learning; Computer Based Modeling at Northwestern University. http://ccl.northwestern.edu/netlogo/models/Flocking

Wissel, C. (1992). Modelling the mosaic cycle of a Middle European beech forest. Ecological Modelling, 63(1), 29–43. https://doi.org/10.1016/0304-3800(92)90060-R

Thank you!